An estimate for derivative of the de la Vallee Poussin mean

In this paper, we discuss derivative of the de la Vallee Poussin mean for exponential weights on real line. When we lead an inequality, an estimate for the Christoffel function plays an important role.Comment: 18 page

Experimental study of sulfur isotope exchange between S0(4)(2-) and H(2)S (aqueous) at 400℃ and 1000 bars water pressure

Experimental procedures used in this study are the same as those developed by Sakai and Dickson (1978). 0.005 M Na(2)S(2)O(3) solutions were heated to 400℃ under 1000 bar water pressure in a gold bag of Dickson gold-bag equipment (Fig. 1). At an elevated temperature Na(2)S(2)O(3) quickly and completely decomposed into 1:1 mixture of SO(4)(2-) and H(2)S (eq. (1)) and subsequent isotope exchange (eq. (2)) was monitored by consecutively withdrawing aliquots of solution for chemical and isotopic analyses at desired time intervals. For the preparation of SO(2) for isotope analyses, 2 to 5 mg BaSO(4) was thoroughly mixed with silica glass powder of 10 times the BaSO(4) in weight and heated to 1400℃ or so in sealed, evacuated silica glass tubings (see Fig. 2 and equation (4)). The technique is a modification of Holt and Engelkemeir (1971). The (18)O/(16)O ratios of SO(2) thus formed stayed constant by exchange with silica glass powder (Fig. 3). Numerical data of the three runs performed in this study are summarized in Tables 1 to 3. In runs 2 and 3, a small aliquot of (34)S- enriched H(2)SO(4) was added into the starting solution and thus equilibrium was approached from above the quilibrium value (see Fig. 4). When isotope exchange occurs between two molecules, X and Y, the reaction rate, r, is related to the extent of exchange, F, at given time, t, by equation (17), where X and Y indicate concentrations of given species, α(e), α(o) and α denote the　fractionation factor at equilibrium, at time　t=0 and at an arbitrary time t, and F = (α - α(o))/(α(e) - α(0)) or the extent of isotope exchange. Assuming the exchange rate is of the first order with respect to both X and Y and to the β'th power of hydrogen ion activity, a(H)(+), eq. (17) reduces to eq. (19), where k(1) denotes the rate constant. If X, Y and pH of solution stayed constant during the run, the half-time, t(1/2), of the exchange reaction can be obtained graphically as shown in Fig. 5. The t(1/2) for runs 1, 2, and 3 are determined to be 5.8, 5.5 and 6.1 hrs, respectively. Introducing F=0.5 and t=t(1/2) into eq. (19), we obtain eq. (20) which is graphically shown in Fig. 6 using the data by the present work and those by Sakai and Dickson(1978). The numerical values of log k(1) + 0.16 may be obtained by extrapolating the lines to pH=0 and, from these values, the rate constant, k(1) , may be calculated for temperatures of 300° and 400℃. From these two values of k(1) and from the Arrhenius plot, the activation energy of the exchange reaction was calculated to be 22 kcal/mole, a much smaller value than 55 kcal/mole obtained by Igumnov (1977). The value of β is found to be 0.29 at 300℃ and 0.075 at 400℃, although the physico-chemical nature of β is not clear to the present authors. Using these values, eq. (24), where C is a constant, is derived which would enable us to calculate the t(1/2) of any system of known ΣS and pH. However, as we do not know yet how β varies with different systems, eq. (24) is applicable only to limited systems in which temperature, total sulfur contents and pH are similar to those of the present study. Fig. 7 illustrates how t(1/2) varies with pH and total sulfur content at 300° and 400℃ and predicts t(1/2) for some solutions obtainable by hydrothermal reactions of seawater with various igneous rocks. The average equilibrium fractionation factor at 400℃ obtained by this study is 1.0153, in good accord with 1.0151 given by Igumnov et al. (1977). Theoretical fractionation factors between SO(4)(2-) and H(2)S have been calculated by Sakai (1968) , who gives too high values compared to the experimental data obtained by this and other researchers (Fig. 9). In the present study, the reduced partition function ratio (R.P.F.R.) of SO(4)(2-) was recalculated using two sets of the vibrational frequencies of SO(4)(2-) (shown in Table 5) and the valence force fields of Heath and Linnett (1947), which reproduces the observed frequencies of SO(4)(2-) better than Urey-Bradley force field used by Sakai (1968). The results of new calculation are shown in Table 6. This table also includes the R.P.F.R. of H(2)S which was calculated by Thode et al. (1971). Using these new R.P.F.R. of SO(4)(2-) and H(2)S, the fractionation factors between SO(4)(2-) and H(2)S were calculated and are listed in the last column of Table 6 and plotted in Fig. 9. Fig. 9 indicates that the new calculation gives values more shifted from the experimental values than before. The major sulfate ions in our solution at 300° and 400℃ exist as NaSO(4)(-) (Sakai and Dickson, 1978; see also Table 4 of this paper) and, therefore, the measured fractionation factors are those between NaSO(4)(-) and H(2)S. The discrepancy between the theory and experiments may, at least, be partially explained by this fact, although other more important reasons, which are not known to us at the moment, may also exist

Clarifying the Pathophysiological Mechanisms of Neuronal Abnormalities of NF1 by Induced-Neuronal (iN) Cells from Human Fibroblasts

Direct conversion techniques, which generate induced-neuronal (iN) cells from human fibroblasts in less than two weeks, are expected to discover unknown neuronal phenotypes of neuropsychiatric disorders. Here, we present unique gene expression and cell morphology profiles in iN cells derived from neurofibromatosis type 1 (NF1) patients. NF1 is a single-gene multifaceted disorder with relatively high co-occurrence of autism spectrum disorder (ASD). Adenylyl cyclase (AC) dysfunction is one of the candidate pathways in abnormal neuronal development in the brains of NF1 patients. In our study, microarray-based transcriptomic analysis of iN cells from healthy controls (males) and NF1 patients (males) revealed significantly different gene expression of 149 (110 were upregulated and 39 were downregulated). In iN cells derived from NF1 patients (NF1-iN cells), there was a change in the expression level of 90 genes with the addition of forskolin, an AC activator. Furthermore, treatment with forskolin dramatically changed the cell morphology, especially that of NF1-iN cells, from flat-form to spherical-form. Current pilot data indicate the potential therapeutic effect of forskolin or AC activators on neuronal growth in NF1 patients. Further translational research is needed to validate the pilot findings for future drug development of ASD

Detailed evaluation of the upper airway in the Dp(16)1Yey mouse model of Down syndrome

A high prevalence of obstructive sleep apnea (OSA) has been reported in Down syndrome (DS) owing to the coexistence of multiple predisposing factors related to its genetic abnormality, posing a challenge for the management of OSA. We hypothesized that DS mice recapitulate craniofacial abnormalities and upper airway obstruction of human DS and can serve as an experimental platform for OSA research. This study, thus, aimed to quantitatively characterize the upper airway as well as craniofacial abnormalities in Dp(16)1Yey (Dp16) mice. Dp16 mice demonstrated craniofacial hypoplasia, especially in the ventral part of the skull and the mandible, and rostrally positioned hyoid. These changes were accompanied with a shorter length and smaller cross-sectional area of the upper airway, resulting in a significantly reduced upper airway volume in Dp16 mice. Our non-invasive approach, a combination of computational fluid dynamics and high-resolution micro-CT imaging, revealed a higher negative pressure inside the airway of Dp16 mice compared to wild-type littermates, showing the potential risk of upper airway collapse. Our study indicated that Dp16 mice can be a useful model to examine the pathophysiology of increased upper airway collapsibility of DS and to evaluate the efficacy of therapeutic interventions for breathing and sleep anomalies

雄性マウス頭蓋内肥満細胞が担う社会性行動の調節

Mast cells (MCs) exist intracranially and have been reported to affect higher brain functions in rodents. However, the role of MCs in the regulation of emotionality and social behavior is unclear. In the present study, using male mice, we examined the relationship between MCs and social behavior and investigated the underlying mechanisms. Wild-type male mice intraventricularly injected with a degranulator of MCs exhibited a marked increase in a three-chamber sociability test. In addition, removal of MCs in Mast cell-specific Toxin Receptor-mediated Conditional cell Knock out (Mas-TRECK) male mice showed reduced social preference levels in a three-chamber sociability test without other behavioral changes, such as anxiety-like and depression-like behavior. Mas-TRECK male mice also had reduced serotonin content and serotonin receptor expression and increased oxytocin receptor expression in the brain. These results suggested that MCs may contribute to the regulation of social behavior in male mice. This effect may be partially mediated by serotonin derived from MCs in the brain